Topological Polynomials in Fuzzy Hamiltonian Graph

A fuzzy graph G = (σ, µ) is a pair of functions of membership values of vertices and edges. A fuzzy Hamiltonian graph is a connected fuzzy graph containing a fuzzy cycle that visits every vertex exactly once, except for the starting and ending vertex coincide. The first and second Zagreb polynomial for fuzzy Hamiltonian graph are defined as:M1(G,x) =and M2(G,x)= respectively, where is the degree of the vertex u and is the membership value of the vertex u in G. In this paper first, second Zagreb polynomials, hyper first, second Zagreb polynomials, forgotten polynomial, harmonic polynomial and Randic polynomial are investigated for fuzzy Hamiltonian graph.